This is one of those ones where you need to separate fact from fiction and try and the truth. Every actor or actress will tell you "I almost had this role or that role" because they auditioned for it and that is where a lot of the trouble starts and they can also be the worst people with memories of how things unfold. Unless there is video of the audition? I do not believe it. Many of the stories of "almost" casting comes from suits and ties trying to push their clients or someone who the thought would make it a blockbuster.
For Independence day Ethen Hawks was riding shotgun in car driving down the highway, reading the script and said this was bullshit and tossed the script out the window. The assumption he made and other people made was that it was the Will Smith role--back when it came Jerry B said they want him for the Jeff Goldbloom role not the Will Smith role
That said, here are a few
Recent one is Spielberg's Lincoln. Danial Day Lewis made the role his own. But up to about 6 months before they started filming, Liam Neeson had actually agreed to do the movie and reportedly had read every book on the subject. The movie had been in production hell for about 10 years. Then DDL got involved and the movie came out of production hell. Spielberg has said that there was something missing until DDL came in and another writer joined and then it all came together.
Hugh Grant was offered a chance to replace Charlie Sheen in two and half men. He names a price and they agreed--he then asked to see the script. There was none. The said sign the deal and we will figure things out. He said before he signed he wanted to see some scripts and there were none so he backed out
The Untouchables: Both De Palma and Bob Hoskins tell the same story. De Niro was always the first choice for the role but he turned it flat. So Hoskins got cast. Hoskins was signed. At the 11th hour, De Nino decides to do it. Hoskins is out and still get paid the money he had signed to do the movie. Hoskins great line after getting paid "Feel free to pay me for another movie you do not want me to be in"
Indiana Jones: Tom Selleck was supposed to do it but he had shot the pilot for Magnum PI and he was supposed to film it. There was a TV actors strike that shutdown the tv side of things. This was before union combined both sides because it was confusing. Selleck had signed on to Raiders of the lost ark. Due to it was movie contract and not a TV contract. HE could of done it. I believe it was around 1990 that the line was removed were TV and motion picture both fell under the same contract law. Of course we know who became Indiana Jones (fun fact Tom Selleck's agent was Betty McCatt who was Albert Ruddy's assistant/office manager during the shooting of the God Father--she was his agent from 1974 till her death in 2013)
The movie the Outsiders from 1983 is one of Francis Ford Coppola most underrated movies. Every actor under 22 auditioned for different roles(they are on youtube) Adam Baldwin was nearly cast Dallas in the movie but FCC started playing mix and matching of different young actors and when Matt Dillon read with Ralph Machio, Esteves and Cruise and he got the role.
Mark Hamill was in the pilot for Eight is Enough and was suppose to be the oldest son. He was offered Star Wars was about to turn it down when the suits decided he was not "big" enough for the oldest brother and hired Goodeve and that freed up Hamil.
Another FCC movie was Apocalypse now. One of the most trouble shoots of all time. Harvey Keitel filmed a few weeks on set before being replaces by Martin Sheen. Both FCC and Keitel's versions of events of why he got sacked. Both Keitel and Sheen are method actors, but Keitel sometimes took it to the extreme. Also, Keitel did 3 years in the Marines and used his experience serving in Lebanon and a few other places for his role--FCC did not like that. And according to Keitel? HE may have had a little problem with some white powder and was a very intense individual--nothing like the passive Sheen style.
a few years ago we finally got some photos of Keitel on the set as FCC reportedly burned all the film of Keitel